Using fluorescence recovery after photobleaching (FRAP), we have previously shown that the GFP-tagged glucocorticoid receptor is bound at a specific promoter for at most 60 seconds, even though transcription persists for several hours. Similar results have now been observed for a number of other transcription factors and for a variety of other nuclear proteins. These in vivo measurements are in many cases very different from measurements made in the test tube which typically have indicated that nuclear proteins, including transcription factors, are much more stably bound. Thus to understand how these proteins function in live cells it is critically important to measure their residence times on chromatin and see how this relates to their functions on chromatin. For the case of transcription factors, this question translates to how does the transcription factor residence time relate to the amount of transcript produced from genes to which the transcription factor binds.In order to address these questions we have been developing methods to measure residence times of transcription factors on chromatin within live cells. We initially used the data from fluorescence recovery after photobleaching data (FRAP) combined with mathematical models of this experiment to obtain estimates of transcription factor residence times on chromatin. However, other groups using similar analysis procedures obtained very different estimates, and so we investigated the source of this discrepancy. We found that many different mathematical models could fit the same FRAP data, and so yield very different residence times. By evaluating these different modeling approaches, we showed how false assumptions in some of the models led to significant errors in the estimation of residence times. This led us to propose a more robust approach to make these measurements by FRAP analysis.To validate our FRAP protocol, we developed an alternative approach using fluorescence correlation spectroscopy (FCS), which we showed is also capable of measuring binding of a transcription factor to chromatin. By comparing the FCS analysis with the FRAP analysis we identified errors in the FCS analysis that we were able to correct and so achieve good agreement between the estimates of residence times by FRAP and FCS.A limitation of both FRAP and FCS is that they rely on mathematical models to describe changes in fluorescence intensity that arise due to at least two underlying processes, diffusion and binding. Neither process can be directly visualized by FRAP or FCS, so an incorrect assumption about how diffusion occurs can lead to an error in the estimates of binding. To evaluate more directly how diffusion and binding occur in the nucleus we have developed methods for single molecule tracking of transcription factors in live cell nuclei. This approach makes it easier to distinguish diffusion from binding since single molecules bound to chromatin move much less than molecules that diffuse through the nucleoplasm. Using this approach, we have shown that the measured residence times by single molecule tracking are close to those measured by FRAP and FCS for the transcription factor p53. This reasonable agreement among three different methods for the measurement of live cell binding suggests that we can now make these measurements reasonably accurately. This will allow us to direct our attention to how transcription factor residence times affect transcription.To obtain a precise estimate of how long the glucocorticoid receptor remains bound to the promoter, we have developed mathematical models to analyze the diffusion and binding interactions of the receptor that occur during the fluorescent recovery after photobleaching experiment. Our model predicts that individual glucocorticoid receptors are bound at the promoter for less than a second. This very transient binding raises new questions about how the transcription complex can be assembled with such short residence times of the transcription factor. At the same time, we have shown that different analysis procedures for fluorescence recovery after photobleaching can yield different estimates of residence times. This shows that there are still uncertainties in the estimation of live cell binding parameters that will require developing alternate measurement procedures to arrive at consensus estimates.Towards this end, we have now developed a mathematical model to extract binding estimates from fluorescence correlation spectroscopy data, and used this to compare binding estimates obtained for the same molecule by fluorescence recovery after photobleaching and by flourescence correlation spectroscopy. We have shown that the two approaches agree, but only if a correction is made in the standard approach for fluorescence correlation spectroscopy. The correction must account for the bleaching which occurs during the measurement process. Thus, our cross validation procedure has helped to identify an error in one of the procedures, and at the same time has helped increase our confidence in our current live cell binding estimates. We have also extended these live cell binding procedures to examine cooperative interactions of a single molecule inside of a live cell. For this purpose, we used the linker histone H1 and analyzed its binding to chromatin by using our analysis procedures to estimate the fraction of bound H1 molecules. We did this for the wild type H1 molecule as well as for a series of mutants that lack various key binding domains. By comparing the fraction of molecules bound in the different mutants, we could determine which domains interact cooperatively in the binding process. In simple terms, cooperatively interacting domains are those for which a much higher fraction is bound when both are present compared to the sum of the bound fractions when either is present by itself. This procedure will be a generally useful one for investigating cooperative binding of molecules in live cells.Finally, we have developed single molecule tracking techniques to monitor transcription factor movement inside of live cell nuclei. We are using this procedure to estimate the binding residence times of transcription factors by measuring how long they remain immobile. This reflects the time that they are bound to chromatin. Preliminary data indicate that these times are somewhat faster by a factor of 2-5 than the residence times measured by fluorescence correlation spectroscopy and fluorescence recovery after photobleaching. The difference may be due to complex diffusion processes revealed by single molecule tracking which are not incorporated into the models used to analyze fluorescence correlation spectroscopy or fluorescence recovery after photobleaching.